# How to Add and Subtract Positive and Negative Numbers

## Numbers Can be Positive or Negative:

 Negative Numbers (−) Positive Numbers (+) (This is the Number Line, read about Using The Number Line)

 "−" is the negative sign. "+" is the positive sign

## No Sign Means Positive

If a number has no sign it usually means that it is a positive number.

Example: 5 is really +5

### Example: 2 + 3 = 5

is really saying

"Positive 2 plus Positive 3 equals Positive 5"

You could write it as (+2) + (+3) = (+5)

### Subtracting Positive Numbers

Subtracting positive numbers is just simple subtraction.

### Example: 6 − 3 = 3

is really saying

"Positive 6 minus Positive 3 equals Positive 3"

You could write it as (+6) − (+3) = (+3)

## Balloons and Weights

 This basket has balloons and weights tied to it: The balloons pull up (positive) And the weights drag down (negative)

Here is what adding and subtracting positive numbers looks like:

 You can take away balloons (you are subtracting positive value) the basket gets pulled downwards (negative)

Now let's see what adding and subtracting negative numbers looks like:

 And you can take away weights (you are subtracting negative values) the basket gets pulled upwards (positive)

That last one was interesting ... subtracting a negative made the basket go up

 Subtracting a Negative is the same as Adding

### Example: What is 6 − (−3) ?

6−(−3) = 6 + 3 = 9

### Example: What is 14 − (−4) ?

14−(−4) = 14 + 4 = 18

## And Positive and Negative Together ...

 Subtracting a Positive or Adding a Negative is Subtraction

6−(+3) = 6 3 = 3

### Example: What is 5 + (−7) ?

5+(−7) = 5 7 = −2

## The Rules:

It can all be put into two rules:

Rule Example +(+) Two like signs become a positive sign 3+(+2) = 3 + 2 = 5 6−(−3) = 6 + 3 = 9 Two unlike signs become a negative sign 7+(−2) = 7 − 2 = 5 8−(+2) = 8 − 2 = 6

They are "like signs" when they are like each other (in other words: the same).

So, all you have to remember is:

Two like signs become a positive sign

Two unlike signs become a negative sign

### Example: What is 5+(−2) ?

+(−) are unlike signs (they are not the same), so they become a negative sign.

5+(−2) = 5 2 = 3

### Example: What is 25−(−4) ?

−(−) are like signs, so they become a positive sign.

25−(−4) = 25+4 = 29

### Example: What is −6+(+3) ?

+(+) are like signs, so they become a positive sign.

−6+(+3) = −6 + 3 = -3

Start at −6 on the number line, move forward 3, and you end up at −3

## Now Play With It!

 Try playing Casey Runner, you need to know the rules of positive and negative to succeed!

## A Common Sense Explanation

And there is a "common sense" explanation:

If I say "Eat!" I am encouraging you to eat (positive)

But if I say "Do not eat!" I am saying the opposite (negative).

Now if I say "Do NOT not eat!", I am saying I don't want you to starve, so I am back to saying "Eat!" (positive).

So, two negatives make a positive, and if that satisfies you, then you are done!

## Another Common Sense Explanation

A friend is +, an enemy is

 + + ⇒ + a friend of a friend is my friend + − ⇒ − a friend of an enemy is my enemy − + ⇒ − an enemy of a friend is my enemy − − ⇒ + an enemy of an enemy is my friend

## A Bank Example

### Last year the bank subtracted \$10 by mistake, and they want to fix it.

So the bank must take away a negative \$10:

\$80−(−\$10) = \$80 + \$10 = \$90

So you get \$10 more in your account.

## Another Example You Might Like

### Ally's Points

 Ally can be naughty or nice. So Ally's parents have said "If you are nice we will add 3 points (+3). If you are naughty, we take away 3 points (−3). When you reach 30 Points you get a toy." Ally starts the day with 9 Points:

 Ally's Mom discovers spilt milk: 9−3 = 6 Then Dad confesses he spilt the milk and writes "undo". Mom calculates: 6−(−3) = 6+3 = 9

So if you subtract a negative, you gain points
(i.e. the same as adding points).

 So Subtracting a Negative is the same as Adding

 A few days later. Ally has 12 points. Mom adds 3 points because Ally's room is clean. 12+3 = 15 Dad says "I cleaned that room" and writes "undo" on the chart. Mom calculates: 15 − (+3) = 12 Dad sees Ally brushing the dog. Writes "+3" on the chart. Mom calculates: 12 + (+3) = 15 Ally throws a stone against the window. Dad writes "−3" on the chart. Mom calculates: 15 + (−3) = 12

See: both "15 − (+3)" and "15 + (−3)" result in 12.

So:

It doesn't matter if you subtract positive points